Final answer:
To eliminate null productions from a grammar, identify the nullable variables, create new productions for other rules by omitting nullable variables, and then remove the original null production. Applying this to the example provided, we successfully removed the null production to ensure no production rules yield an empty string.
Step-by-step explanation:
To eliminate null productions from context-free grammar, we need to modify the production rules so that they no longer produce an empty string (represented by ε). Considering the grammar provided:
S → a4bCCABA
A → Ba | bA | AB | ε
B → a | A
We can see that A can produce ε and thus is a nullable variable. To eliminate this null production, we proceed as follows:
Identify the nullable variables. Here, A is nullable because A → ε.
For each occurrence of a nullable variable in other production rules, create new productions by omitting that nullable variable. Do this for all possible combinations.
Remove the original nullable production rule (A → ε) after creating the new productions.
Applying these steps:
S → a4bCCB | a4bCC
A → Ba | b | B | bA
B → a | Ba | b
Now the grammar does not have any null productions.